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Vampire-SAT---5.0.1.UNS-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SWC420-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 01:05:59 PM UTC 2026

% Result   : Unsatisfiable 5.19s 1.05s
% Output   : Refutation 5.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  111 (  22 unt;   8 def)
%            Number of atoms       :  334 (  53 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  449 ( 226   ~; 215   |;   0   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   14 (  12 usr;   9 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   94 (   0 sgn  94   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).

fof(f9,axiom,
    ssItem(skac3),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause9) ).

fof(f72,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).

fof(f73,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).

fof(f74,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(tl(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).

fof(f85,axiom,
    ! [X0,X1] :
      ( ssList(app(X1,X0))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).

fof(f86,axiom,
    ! [X0,X1] :
      ( ssList(cons(X0,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).

fof(f107,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | cons(hd(X0),tl(X0)) = X0
      | nil = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).

fof(f118,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).

fof(f125,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | app(cons(X0,nil),X1) = cons(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | cons(X0,X1) = app(cons(X0,nil),X1) ),
    inference(reorient_equations,[],[f125]) ).

fof(f193,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ duplicatefreeP(X4)
      | ~ ssList(X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).

fof(f202,negated_conjecture,
    ssList(sk3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).

fof(f203,negated_conjecture,
    ssList(sk4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).

fof(f204,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).

fof(f205,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

fof(f206,negated_conjecture,
    neq(sk2,nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

fof(f207,negated_conjecture,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | app(app(X1,cons(X0,nil)),X2) != sk2
      | app(app(X2,cons(X0,nil)),X1) != sk1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

fof(f208,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | sk2 != app(app(X1,cons(X0,nil)),X2)
      | sk1 != app(app(X2,cons(X0,nil)),X1) ),
    inference(reorient_equations,[],[f207]) ).

fof(f209,negated_conjecture,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | app(X1,cons(X0,nil)) = sk3
      | app(cons(X0,nil),X1) != sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

fof(f210,plain,
    ! [X0,X1] :
      ( app(cons(X0,nil),X1) != sk4
      | ~ ssList(X1)
      | sk3 = app(X1,cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(reorient_equations,[],[f209]) ).

fof(f214,plain,
    neq(sk4,nil),
    inference(definition_unfolding,[],[f206,f204]) ).

fof(f215,plain,
    ! [X2,X0,X1] :
      ( sk4 != app(app(X1,cons(X0,nil)),X2)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssItem(X0)
      | sk3 != app(app(X2,cons(X0,nil)),X1) ),
    inference(definition_unfolding,[],[f208,f204,f205]) ).

fof(f222,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f118]) ).

fof(f233,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssList(X3) ),
    inference(equality_resolution,[],[f193]) ).

fof(f244,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f222]) ).

fof(f247,definition,
    ( spl0_1
  <=> ! [X0] : ~ ssItem(X0) ),
    introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).

fof(f248,plain,
    ( ! [X0] : ~ ssItem(X0)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f247]) ).

fof(f250,definition,
    ( spl0_2
  <=> ! [X1] : ~ ssList(X1) ),
    introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).

fof(f251,plain,
    ( ! [X1] : ~ ssList(X1)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f258,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[],[f202,f251]) ).

fof(f259,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f258]) ).

fof(f264,definition,
    ( spl0_6
  <=> nil = sk4 ),
    introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).

fof(f265,plain,
    ( nil = sk4
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f266,plain,
    ( nil != sk4
    | spl0_6 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f272,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[],[f9,f248]) ).

fof(f273,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f272]) ).

fof(f390,definition,
    ( spl0_36
  <=> ! [X1] : ssItem(X1) ),
    introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).

fof(f391,plain,
    ( ! [X1] : ssItem(X1)
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f390]) ).

fof(f396,definition,
    ( spl0_38
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).

fof(f397,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f396]) ).

fof(f398,plain,
    ( spl0_36
    | spl0_38 ),
    inference(avatar_split_clause,[],[f72,f396,f390]) ).

fof(f432,plain,
    sk3 = app(sk3,nil),
    inference(resolution,[],[f73,f202]) ).

fof(f961,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(app(X0,cons(X1,X2)))
      | ~ ssList(cons(X1,X3))
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssList(X3) ),
    inference(resolution,[],[f85,f233]) ).

fof(f1321,plain,
    ! [X2,X3,X0,X1] :
      ( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssList(app(X0,cons(X1,X2)))
      | ~ ssList(X3) ),
    inference(forward_subsumption_resolution,[],[f961,f86]) ).

fof(f1348,definition,
    ( spl0_55
  <=> ! [X2,X0,X1] :
        ( ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssItem(X1)
        | ~ ssList(X0)
        | ~ ssList(X2) ) ),
    introduced(definition,[new_symbols(definition,[spl0_55])],[avatar_definition]) ).

fof(f1349,plain,
    ( ! [X2,X0,X1] :
        ( ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssItem(X1)
        | ~ ssList(X0)
        | ~ ssList(X2) )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f1348]) ).

fof(f1351,plain,
    ( ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(cons(X0,X2)) )
    | ~ spl0_55 ),
    inference(resolution,[],[f1349,f85]) ).

fof(f1352,plain,
    ( ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssList(cons(X0,X2)) )
    | ~ spl0_55 ),
    inference(duplicate_literal_removal,[],[f1351]) ).

fof(f1353,plain,
    ( ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ ssList(X2) )
    | ~ spl0_55 ),
    inference(forward_subsumption_resolution,[],[f1352,f86]) ).

fof(f1354,plain,
    ( spl0_2
    | spl0_2
    | spl0_1
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1353,f1348,f247,f250,f250]) ).

fof(f1384,plain,
    ( ! [X0,X1] :
        ( duplicatefreeP(app(X0,X1))
        | ~ ssList(X0)
        | ~ ssList(X1) )
    | ~ spl0_38 ),
    inference(resolution,[],[f397,f85]) ).

fof(f1393,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssList(cons(X1,X3))
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssList(X3) )
    | ~ spl0_38 ),
    inference(resolution,[],[f1384,f1321]) ).

fof(f1444,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssList(cons(X1,X3))
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssList(X3) )
    | ~ spl0_38 ),
    inference(duplicate_literal_removal,[],[f1393]) ).

fof(f1445,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssList(X3) )
    | ~ spl0_38 ),
    inference(forward_subsumption_resolution,[],[f1444,f86]) ).

fof(f1459,plain,
    ( spl0_2
    | spl0_55
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f1445,f396,f1348,f250]) ).

fof(f4756,plain,
    ( sk4 = cons(hd(sk4),tl(sk4))
    | nil = sk4 ),
    inference(resolution,[],[f107,f203]) ).

fof(f4808,definition,
    ( spl0_153
  <=> ssList(tl(sk4)) ),
    introduced(definition,[new_symbols(definition,[spl0_153])],[avatar_definition]) ).

fof(f4809,plain,
    ( ssList(tl(sk4))
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f4808]) ).

fof(f4810,plain,
    ( ~ ssList(tl(sk4))
    | spl0_153 ),
    inference(avatar_component_clause,[],[f4808]) ).

fof(f4821,plain,
    ( ~ ssList(sk4)
    | nil = sk4
    | spl0_153 ),
    inference(resolution,[],[f4810,f75]) ).

fof(f4822,plain,
    ( nil = sk4
    | spl0_153 ),
    inference(forward_subsumption_resolution,[],[f4821,f203]) ).

fof(f4823,plain,
    ( $false
    | spl0_6
    | spl0_153 ),
    inference(forward_subsumption_resolution,[],[f4822,f266]) ).

fof(f4824,plain,
    ( spl0_6
    | spl0_153 ),
    inference(avatar_contradiction_clause,[],[f4823]) ).

fof(f5566,plain,
    ( neq(nil,nil)
    | ~ spl0_6 ),
    inference(superposition,[],[f214,f265]) ).

fof(f5631,plain,
    ( ~ ssList(nil)
    | ~ spl0_6 ),
    inference(resolution,[],[f5566,f244]) ).

fof(f5632,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[],[f5631,f8]) ).

fof(f5633,plain,
    ~ spl0_6,
    inference(avatar_contradiction_clause,[],[f5632]) ).

fof(f5657,plain,
    ( sk4 = cons(hd(sk4),tl(sk4))
    | spl0_6 ),
    inference(forward_subsumption_resolution,[],[f4756,f266]) ).

fof(f7918,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) )
    | ~ spl0_36 ),
    inference(forward_subsumption_resolution,[],[f126,f391]) ).

fof(f7954,plain,
    ( ! [X0] : cons(X0,tl(sk4)) = app(cons(X0,nil),tl(sk4))
    | ~ spl0_36
    | ~ spl0_153 ),
    inference(resolution,[],[f7918,f4809]) ).

fof(f8308,plain,
    ( ! [X0] :
        ( sk4 != cons(X0,tl(sk4))
        | ~ ssList(tl(sk4))
        | sk3 = app(tl(sk4),cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_36
    | ~ spl0_153 ),
    inference(superposition,[],[f210,f7954]) ).

fof(f8335,plain,
    ( ! [X0] :
        ( sk4 != cons(X0,tl(sk4))
        | sk3 = app(tl(sk4),cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_36
    | ~ spl0_153 ),
    inference(forward_subsumption_resolution,[],[f8308,f4809]) ).

fof(f8339,plain,
    ( ! [X0] :
        ( sk4 != cons(X0,tl(sk4))
        | sk3 = app(tl(sk4),cons(X0,nil)) )
    | ~ spl0_36
    | ~ spl0_153 ),
    inference(forward_subsumption_resolution,[],[f8335,f391]) ).

fof(f14727,plain,
    ( sk4 != sk4
    | sk3 = app(tl(sk4),cons(hd(sk4),nil))
    | spl0_6
    | ~ spl0_36
    | ~ spl0_153 ),
    inference(superposition,[],[f8339,f5657]) ).

fof(f14728,plain,
    ( sk3 = app(tl(sk4),cons(hd(sk4),nil))
    | spl0_6
    | ~ spl0_36
    | ~ spl0_153 ),
    inference(trivial_inequality_removal,[],[f14727]) ).

fof(f17268,definition,
    ( spl0_318
  <=> ssList(cons(hd(sk4),nil)) ),
    introduced(definition,[new_symbols(definition,[spl0_318])],[avatar_definition]) ).

fof(f17269,plain,
    ( ssList(cons(hd(sk4),nil))
    | ~ spl0_318 ),
    inference(avatar_component_clause,[],[f17268]) ).

fof(f17270,plain,
    ( ~ ssList(cons(hd(sk4),nil))
    | spl0_318 ),
    inference(avatar_component_clause,[],[f17268]) ).

fof(f17272,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk4))
    | spl0_318 ),
    inference(resolution,[],[f17270,f86]) ).

fof(f17273,plain,
    ( ~ ssItem(hd(sk4))
    | spl0_318 ),
    inference(forward_subsumption_resolution,[],[f17272,f8]) ).

fof(f17274,plain,
    ( $false
    | ~ spl0_36
    | spl0_318 ),
    inference(forward_subsumption_resolution,[],[f17273,f391]) ).

fof(f17275,plain,
    ( ~ spl0_36
    | spl0_318 ),
    inference(avatar_contradiction_clause,[],[f17274]) ).

fof(f17867,plain,
    ( cons(hd(sk4),nil) = app(nil,cons(hd(sk4),nil))
    | ~ spl0_318 ),
    inference(resolution,[],[f17269,f74]) ).

fof(f19763,plain,
    ( ! [X0] :
        ( sk4 != app(cons(hd(sk4),nil),X0)
        | ~ ssList(nil)
        | ~ ssList(X0)
        | ~ ssItem(hd(sk4))
        | sk3 != app(app(X0,cons(hd(sk4),nil)),nil) )
    | ~ spl0_318 ),
    inference(superposition,[],[f215,f17867]) ).

fof(f19815,plain,
    ( ! [X0] :
        ( sk4 != app(cons(hd(sk4),nil),X0)
        | ~ ssList(X0)
        | ~ ssItem(hd(sk4))
        | sk3 != app(app(X0,cons(hd(sk4),nil)),nil) )
    | ~ spl0_318 ),
    inference(forward_subsumption_resolution,[],[f19763,f8]) ).

fof(f19827,plain,
    ( ! [X0] :
        ( sk3 != app(app(X0,cons(hd(sk4),nil)),nil)
        | ~ ssList(X0)
        | sk4 != app(cons(hd(sk4),nil),X0) )
    | ~ spl0_36
    | ~ spl0_318 ),
    inference(forward_subsumption_resolution,[],[f19815,f391]) ).

fof(f19913,plain,
    ( sk3 != app(sk3,nil)
    | ~ ssList(tl(sk4))
    | sk4 != app(cons(hd(sk4),nil),tl(sk4))
    | spl0_6
    | ~ spl0_36
    | ~ spl0_153
    | ~ spl0_318 ),
    inference(superposition,[],[f19827,f14728]) ).

fof(f19916,plain,
    ( ~ ssList(tl(sk4))
    | sk4 != app(cons(hd(sk4),nil),tl(sk4))
    | spl0_6
    | ~ spl0_36
    | ~ spl0_153
    | ~ spl0_318 ),
    inference(forward_subsumption_resolution,[],[f19913,f432]) ).

fof(f19918,plain,
    ( sk4 != app(cons(hd(sk4),nil),tl(sk4))
    | spl0_6
    | ~ spl0_36
    | ~ spl0_153
    | ~ spl0_318 ),
    inference(forward_subsumption_resolution,[],[f19916,f4809]) ).

fof(f19920,plain,
    ( sk4 != cons(hd(sk4),tl(sk4))
    | spl0_6
    | ~ spl0_36
    | ~ spl0_153
    | ~ spl0_318 ),
    inference(forward_demodulation,[],[f19918,f7954]) ).

fof(f19921,plain,
    ( $false
    | spl0_6
    | ~ spl0_36
    | ~ spl0_153
    | ~ spl0_318 ),
    inference(forward_subsumption_resolution,[],[f19920,f5657]) ).

fof(f19922,plain,
    ( spl0_6
    | ~ spl0_36
    | ~ spl0_153
    | ~ spl0_318 ),
    inference(avatar_contradiction_clause,[],[f19921]) ).

cnf(s205,plain,
    ~ spl0_2,
    inference(sat_conversion,[],[f259]) ).

cnf(s226,plain,
    ~ spl0_1,
    inference(sat_conversion,[],[f273]) ).

cnf(s382,plain,
    ( spl0_36
    | spl0_38 ),
    inference(sat_conversion,[],[f398]) ).

cnf(s964,plain,
    ( spl0_2
    | spl0_1
    | spl0_2
    | ~ spl0_55 ),
    inference(sat_conversion,[],[f1354]) ).

cnf(s965,plain,
    ( spl0_1
    | spl0_2
    | ~ spl0_55 ),
    inference(rat,[],[s964]) ).

cnf(s1055,plain,
    ( spl0_2
    | ~ spl0_38
    | spl0_55 ),
    inference(sat_conversion,[],[f1459]) ).

cnf(s2661,plain,
    ( spl0_6
    | spl0_153 ),
    inference(sat_conversion,[],[f4824]) ).

cnf(s3106,plain,
    ~ spl0_6,
    inference(sat_conversion,[],[f5633]) ).

cnf(s9420,plain,
    ( ~ spl0_36
    | spl0_318 ),
    inference(sat_conversion,[],[f17275]) ).

cnf(s10764,plain,
    ( spl0_6
    | ~ spl0_36
    | ~ spl0_153
    | ~ spl0_318 ),
    inference(sat_conversion,[],[f19922]) ).

cnf(s10775,plain,
    spl0_153,
    inference(rat,[],[s2661,s3106]) ).

cnf(s10784,plain,
    ~ spl0_55,
    inference(rat,[],[s965,s226,s205]) ).

cnf(s10789,plain,
    ~ spl0_38,
    inference(rat,[],[s1055,s205,s10784]) ).

cnf(s10791,plain,
    spl0_36,
    inference(rat,[],[s382,s10789]) ).

cnf(s10792,plain,
    ~ spl0_318,
    inference(rat,[],[s10764,s10775,s3106,s10791]) ).

cnf(s10807,plain,
    $false,
    inference(rat,[],[s9420,s10792,s10791]) ).

fof(f19923,plain,
    $false,
    inference(avatar_sat_refutation,[],[s10807]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC420-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.27  % Computer : n019.cluster.edu
% 0.14/0.27  % Model    : x86_64 x86_64
% 0.14/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.27  % Memory   : 8046.5625MB
% 0.14/0.27  % OS       : Linux 6.8.0-71-generic
% 0.14/0.27  % CPULimit : 300
% 0.14/0.27  % WCLimit  : 300
% 0.14/0.27  % DateTime : Mon Sep 28 09:35:49 UTC 2026
% 0.14/0.27  % CPUTime  : 
% 0.14/0.27  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.29  Running first-order model finding
% 0.14/0.29  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.19/1.05  % (3875528)Will run a generic schedule for satisfiability detection.
% 5.19/1.05  % (3875538)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1335420672:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.19/1.05  % (3875534)% WARNING: option uhcvi not known.
% 5.19/1.05  % (3875533)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2749932886_2999 on theBenchmark for (2999ds/0Mi)
% 5.19/1.05  % (3875537)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2669792405:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.19/1.05  % (3875535)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=736329422:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.19/1.05  % (3875536)dis+10_1_sil=32000:sp=arity:random_seed=3864908503:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.19/1.05  % (3875539)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3655640110:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.19/1.05  % (3875534)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1880426867:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.19/1.05  % TRYING [1]
% 5.19/1.05  % TRYING [2]
% 5.19/1.05  % TRYING [3]
% 5.19/1.05  % (3875538)Instruction limit reached! 
% 5.19/1.05  % (3875538)------------------------------
% 5.19/1.05  % (3875538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875538)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875538)Termination reason: Instruction limit
% 5.19/1.05  % (3875538)Termination phase: Saturation
% 5.19/1.05  % (3875538)Time elapsed: 0.035 s
% 5.19/1.05  % (3875538)Peak memory usage: 13 MB
% 5.19/1.05  % (3875538)Instructions burned: 132 (million)
% 5.19/1.05  % TRYING [4]
% 5.19/1.05  % (3875547)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4211288096:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.19/1.05  % TRYING [1]
% 5.19/1.05  % TRYING [2]
% 5.19/1.05  % TRYING [3]
% 5.19/1.05  % (3875537)Instruction limit reached! 
% 5.19/1.05  % (3875537)------------------------------
% 5.19/1.05  % (3875537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875537)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875537)Termination reason: Instruction limit
% 5.19/1.05  % (3875537)Termination phase: Saturation
% 5.19/1.05  % (3875537)Time elapsed: 0.060 s
% 5.19/1.05  % (3875537)Peak memory usage: 13 MB
% 5.19/1.05  % (3875537)Instructions burned: 116 (million)
% 5.19/1.05  % (3875536)Instruction limit reached! 
% 5.19/1.05  % (3875536)------------------------------
% 5.19/1.05  % (3875536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875536)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875536)Termination reason: Instruction limit
% 5.19/1.05  % (3875536)Termination phase: Saturation
% 5.19/1.05  % (3875536)Time elapsed: 0.060 s
% 5.19/1.05  % (3875536)Peak memory usage: 13 MB
% 5.19/1.05  % (3875536)Instructions burned: 104 (million)
% 5.19/1.05  % TRYING [4]
% 5.19/1.05  % (3875550)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1729668698:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.19/1.05  % (3875549)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1645522468:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.19/1.05  % TRYING [5]
% 5.19/1.05  % (3875539)Instruction limit reached! 
% 5.19/1.05  % (3875539)------------------------------
% 5.19/1.05  % (3875539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875539)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875539)Termination reason: Instruction limit
% 5.19/1.05  % (3875539)Termination phase: Saturation
% 5.19/1.05  % (3875539)Time elapsed: 0.098 s
% 5.19/1.05  % (3875539)Peak memory usage: 13 MB
% 5.19/1.05  % (3875539)Instructions burned: 165 (million)
% 5.19/1.05  % TRYING [5]
% 5.19/1.05  % (3875553)ott-21_1_sil=16000:fs=off:random_seed=192291796:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.19/1.05  % (3875549)Instruction limit reached! 
% 5.19/1.05  % (3875549)------------------------------
% 5.19/1.05  % (3875549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875549)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875549)Termination reason: Instruction limit
% 5.19/1.05  % (3875549)Termination phase: Saturation
% 5.19/1.05  % (3875549)Time elapsed: 0.070 s
% 5.19/1.05  % (3875549)Peak memory usage: 13 MB
% 5.19/1.05  % (3875549)Instructions burned: 131 (million)
% 5.19/1.05  % (3875555)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2603743976:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.19/1.05  % (3875547)Instruction limit reached! 
% 5.19/1.05  % (3875547)------------------------------
% 5.19/1.05  % (3875547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875547)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875547)Termination reason: Instruction limit
% 5.19/1.05  % (3875547)Termination phase: Finite model building constraint generation
% 5.19/1.05  % (3875547)Time elapsed: 0.151 s
% 5.19/1.05  % (3875547)Peak memory usage: 37 MB
% 5.19/1.05  % (3875547)Instructions burned: 715 (million)
% 5.19/1.05  % (3875557)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=766883921:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 5.19/1.05  % (3875553)Instruction limit reached! 
% 5.19/1.05  % (3875553)------------------------------
% 5.19/1.05  % (3875553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875553)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875553)Termination reason: Instruction limit
% 5.19/1.05  % (3875553)Termination phase: Saturation
% 5.19/1.05  % (3875553)Time elapsed: 0.090 s
% 5.19/1.05  % (3875553)Peak memory usage: 13 MB
% 5.19/1.05  % (3875553)Instructions burned: 180 (million)
% 5.19/1.05  % TRYING [1]
% 5.19/1.05  % TRYING [2]
% 5.19/1.05  % TRYING [3]
% 5.19/1.05  % (3875559)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2085548663:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 5.19/1.05  % TRYING [4]
% 5.19/1.05  % TRYING [6]
% 5.19/1.05  % TRYING [5]
% 5.19/1.05  % (3875557)Instruction limit reached! 
% 5.19/1.05  % (3875557)------------------------------
% 5.19/1.05  % (3875557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875557)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875557)Termination reason: Instruction limit
% 5.19/1.05  % (3875557)Termination phase: Finite model building SAT solving
% 5.19/1.05  % (3875557)Time elapsed: 0.176 s
% 5.19/1.05  % (3875557)Peak memory usage: 22 MB
% 5.19/1.05  % (3875557)Instructions burned: 865 (million)
% 5.19/1.05  % (3875561)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=389673805:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 5.19/1.05  % TRYING [14]
% 5.19/1.05  % (3875550)Instruction limit reached! 
% 5.19/1.05  % (3875550)------------------------------
% 5.19/1.05  % (3875550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875550)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875550)Termination reason: Instruction limit
% 5.19/1.05  % (3875550)Termination phase: Saturation
% 5.19/1.05  % (3875550)Time elapsed: 0.389 s
% 5.19/1.05  % (3875550)Peak memory usage: 19 MB
% 5.19/1.05  % (3875550)Instructions burned: 684 (million)
% 5.19/1.05  % (3875555)Instruction limit reached! 
% 5.19/1.05  % (3875555)------------------------------
% 5.19/1.05  % (3875555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875555)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875555)Termination reason: Instruction limit
% 5.19/1.05  % (3875555)Termination phase: Saturation
% 5.19/1.05  % (3875555)Time elapsed: 0.302 s
% 5.19/1.05  % (3875555)Peak memory usage: 14 MB
% 5.19/1.05  % (3875555)Instructions burned: 479 (million)
% 5.19/1.05  % (3875563)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=213847938:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 5.19/1.05  % (3875564)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3247028183:i=879:kws=inv_precedence:fsr=off_2994 on theBenchmark for (2994ds/879Mi)
% 5.19/1.05  % (3875561)Instruction limit reached! 
% 5.19/1.05  % (3875561)------------------------------
% 5.19/1.05  % (3875561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875561)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875561)Termination reason: Instruction limit
% 5.19/1.05  % (3875561)Termination phase: Finite model building constraint generation
% 5.19/1.05  % (3875561)Time elapsed: 0.181 s
% 5.19/1.05  % (3875561)Peak memory usage: 77 MB
% 5.19/1.05  % (3875561)Instructions burned: 895 (million)
% 5.19/1.05  % (3875567)fmb+10_1_sil=64000:random_seed=1722011078:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 5.19/1.05  % TRYING [1]
% 5.19/1.05  % TRYING [2]
% 5.19/1.05  % TRYING [3]
% 5.19/1.05  % TRYING [4]
% 5.19/1.05  % (3875535) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3875528-3875535"...
% 5.19/1.05  % (3875535)...printing done.
% 5.19/1.05  % (3875535)Refutation found. Thanks to Tanya!
% 5.19/1.05  % SZS status Unsatisfiable for theBenchmark
% 5.19/1.05  % SZS output start Proof for theBenchmark
% See solution above
% 5.19/1.05  % (3875535)------------------------------
% 5.19/1.05  % (3875535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.05  % (3875535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.05  % (3875535)CaDiCaL version: 2.1.3
% 5.19/1.05  % (3875535)Termination reason: Refutation
% 5.19/1.05  % (3875535)Time elapsed: 0.698 s
% 5.19/1.05  % (3875535)Peak memory usage: 23 MB
% 5.19/1.05  % (3875535)Instructions burned: 1171 (million)
% 5.19/1.05  % (3875528)Success in time 0.747 s
% 5.19/1.05  % Vampire exiting
%------------------------------------------------------------------------------